- Quadratic Functions(General Form)
- (10.2.1) – Identify characteristics of a parabola
- Graphing Quadratic Equations
Quadratic Functions(General Form)
9.1: Quadratic Graphs and their Propertiesand
Let's see an example. Method 2: Using the "sneaky tidbit", seen above, to convert to vertex form:. Graphing a Quadratic Function in Vertex Form:. For this problem, we chose to the left of the axis of symmetry :. Since we will be " completing the square " we will isolate the x 2 and x terms
Form G. Quadratic Graphs and Their Properties. Identify the vertex of each graph Order each group of quadratic functions from widest to narrowest graph.
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The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape. The picture below shows three graphs, and they are all parabolas. All parabolas are symmetric with respect to a line called the axis of symmetry. A parabola intersects its axis of symmetry at a point called the vertex of the parabola.
A function describes a specific relationship between two variables; where an independent input variable has exactly one dependent output variable. Every element in the domain maps to only one element in the range. Functions can be one-to-one relations or many-to-one relations. A many-to-one relation associates two or more values of the independent variable with a single value of the dependent variable. Functions allow us to visualise relationships in the form of graphs, which are much easier to read and interpret than lists of numbers. High marks in maths are the key to your success and future plans.
A quadratic function is a polynomial function of degree 2 which can be written in the general form,. Note that the graph is indeed a function as it passes the vertical line test. When graphing parabolas, we want to include certain special points in the graph. The y -intercept is the point where the graph intersects the y -axis. The x -intercepts are the points where the graph intersects the x -axis.
(10.2.1) – Identify characteristics of a parabola
Graphing Quadratic Equations
Figure 1. An array of satellite dishes. Curved antennas, such as the ones shown in Figure , are commonly used to focus microwaves and radio waves to transmit television and telephone signals, as well as satellite and spacecraft communication. The cross-section of the antenna is in the shape of a parabola, which can be described by a quadratic function. In this section, we will investigate quadratic functions, which frequently model problems involving area and projectile motion. Working with quadratic functions can be less complex than working with higher degree functions, so they provide a good opportunity for a detailed study of function behavior.
How to Graph Parabolas
Quadratic Graphs and Their Properties. Standard Form of a Quadratic Function. Problem 1: Identifying a Vertex. What are the coordinates of the vertex of.
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